Limit (cos(1\x))|tan x| x-> .5pi

  • Thread starter Thread starter rambo123
  • Start date Start date
  • Tags Tags
    Limit
rambo123
Messages
2
Reaction score
0

Homework Statement


having a hard time figuring out. I know the answer if infinite but having a hard time proving it

Homework Equations


tan x = cot (.5pi - x) did not help


The Attempt at a Solution


tried substituting t = 1\x got stuck

thanks
 
Physics news on Phys.org
The limit as x goes to what?
 
x goes to (pi)(1\2)

pi 3.14...
 
limx→π/2cos(1/x) exists, so what's left is limx→π/2|tan x|, which is infinite.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Integrate [cosec(30°+x)-cosec(60°+x)] dx in terms of tan x
Replies
3
Views
1K
Calculate the limit cos(x)/sin(x) when x approaches 0
Replies
12
Views
3K
##\lim_{x \to0} \left(\dfrac{1}{\sin^2 x}-\dfrac{1}{x^2}\right)##
Replies
5
Views
2K
Prove that the limit of |x|/x at x=0 DNE
Replies
9
Views
3K
Tan (a + ib) = x + iy, so how is tan (a-ib) = x - iy
Replies
19
Views
5K
Limits and integration problem
Replies
4
Views
1K
Understanding Complex Plane and Finding Arguments: A Scientist's Perspective
Replies
1
Views
1K
Integral of 1/(a sin^2 x + b sin x cos x + c cos^2 x)
Replies
2
Views
2K
Can you handle this integration with limits problem?
Replies
3
Views
2K
Complex numbers. write equation on form "a+bi"
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top